mathr

A collection of rules for deriving perturbed iterations.

Regions surrounding mini-ships.

A fractal like the Mandelbrot set but with absolute values thrown in to the mix.

Model the whole complex plane via the Riemann sphere as an OpenGL cube map.

Keyframe animation and the return of single precision support with OpenGL 3.3 (OpenGL 4 double precision still an option)

Nucleus finding, Misiurewicz point finding, and a bit of guesswork, combine for successful O(period) automatic Julia morphing.

Improving image quality by avoiding catastrophic cancellations.

Worst-case guess improved by a factor of 8.

Highlighting previously invisible periodic properties in the Mandelbrot set.

Finding periodic points in the Mandelbrot set to make annotated images.

Using third-party libraries for acceleration.

Double precision using OpenGL 4 to avoid postpone ugly artifacts.

Inflection mapping for complex quadratic polynomials.

January 12th to February 5th, Centro Conde Duque, Madrid, Spain.

How they did it, as far as I can tell.

Black-and-white flame fractals synchronized with rich ambient drones.

Experimental OpenGL driver used by Pd and Gem with PdLua seems to work mostly fine.

A familiar picture emerges.

Notes on a conjecture of Aaron Klebanoff.

Tracing the boundaries of hyperbolic components.

Piecewise integer recurrence translated to complex function.

Additive blending reveals many things.

Infinite fractal television zoom

Sliced rendering, improved glitch correction, reduced video memory usage, and more.

Big bad bugs been debugged, and nifty features added.

Lots of changes in a short space of time.

Sometimes simple approaches are better.

Automatic glitch correction, zoom sequence rendering, tiled rendering for high resolution or anti-aliasing, ...

Trace a number of probe points in the atom domain.

Combining saved flake images using command line tools.

From many raw 2fold zoom images to one long strip.

A modified bump-mapping approach.

Subdivide only near the boundary.

Around embedded Julia sets in the Mandelbrot set.

Using Newton's method.

Fixing code from 1992.

Rebasing from a reference point.

Handwritten notes on various properties.

An xmas present for someone special.

Conformal mapping using Möbius transformations.

Rewritten in portable C.

A series of approximations result in a simple formula.

Exploring external angles.

Derived from continuous escape time.

Structures in the hairs.

Derived from distance estimation for Julia sets.

Some notes on various aspects of design and potential implementation.

another representation function

cutting and pasting binary digits of external angles

finding tuned branch points

speeding up external ray tracing

Mandelbrot Set explorer using OpenGL 4

New website, new beginnings.

26 images of the Mandelbrot Set

Following distance estimates.

Lots to think about.

Now hopefully more easily installable.

No algorithm to check open set condition.